4.2 State the principle of conservation of linear momentum in words.

Let EAST be the positive direction.
Mass of car, $m_c = m$
Initial velocity of car, $v_{c,i} = +20 \text{ m/s}$
Mass of truck, $m_t = 2m$
Initial velocity of truck, $v_{t,i} = -20 \text{ m/s}$
Since they stick together, their final velocity will be the same, $v_f$.

The negative sign indicates the direction is WEST.

The velocity of the truck-car system immediately after the collision is $\boxed{\text{6.67 m/s WEST}}$.

4.4 On impact the car exerts a force of magnitude $F$ on the truck and experiences an acceleration of magnitude $a$.

4.4.1 Determine, in terms of $F$, the magnitude of the force that the truck exerts on the car on impact. Give a reason for the answer.

The magnitude of the force that the truck exerts on the car is $\boxed{F}$.
Reason: According to Newton's Third Law of Motion, for every action, there is an equal and opposite reaction. The force exerted by the car on the truck is equal in magnitude and opposite in direction to the force exerted by the truck on the car.

4.4.2 Determine, in terms of $a$, the acceleration that the truck experiences on impact. Give a reason for the answer.

The car has mass $m$ and experiences an acceleration of magnitude $a$.
The magnitude of the force exerted on the car by the truck is $F$ (from 4.4.1).

The truck has mass $2m$. Let its acceleration be $a_t$.
The magnitude of the force exerted on the truck by the car is $F$ (given in the question).

The acceleration that the truck experiences on impact is $\boxed{\frac{a}{2}}$.
Reason: According to Newton's Second Law of Motion ($F_{net} = ma$), for the same magnitude of force $F$, an object with twice the mass ($2m$) will experience half the acceleration ($a/2$) compared to an object with mass $m$.

4.4.3 Both drivers are wearing identical seat belts. Which driver is likely to be more severely injured on impact? Explain the answer by referring to acceleration and velocity.

The car driver is likely to be more severely injured.

Explanation:

• The car has a mass of $m$, and the truck has a mass of $2m$.
• From question 4.4.2, the car experiences an acceleration of magnitude $a$, while the truck experiences an acceleration of magnitude $\frac{a}{2}$. This means the car (and its driver) undergoes a greater deceleration during the collision.
• The car's initial velocity is $20 \text{ m/s}$ EAST, and its final velocity is $6.67 \text{ m/s}$ WEST. The magnitude of its change in velocity is $|(-6.67) - 20| = 26.67 \text{ m/s}$.
• The truck's initial velocity is $20 \text{ m/s}$ WEST, and its final velocity is $6.67 \text{ m/s}$ WEST. The magnitude of its change in velocity is $|(-6.67) - (-20)| = |-6.67 + 20| = 13.33 \text{ m/s}$.
• Since the car experiences a larger change in velocity over the same collision time, it also experiences a larger acceleration ($a = \frac{\Delta v}{\Delta t}$). A larger acceleration (deceleration) means a greater force exerted on the driver by the seatbelt, leading to more severe injuries.